An Introduction to Quantum Dots:Confinement, Synthesis, Artificial Atoms andApplicationsJohn SinclairUniveristy of TennesseeSolid State IIInstructer: Dr. DagottoApril 9, 2009AbstractThis paper will introduce ideas of quantum dots. It will focus onthe ideas of quantum confinement and applications of quantum dotsto lasers and biological systems.1 IntroductionNanoscience is a very interesting and technologically relevant area of con-densed matter physics. Quantum dots are one of the zero dimensional sys-tems in this field and the subject this paper will focus on. The paper willintroduce the idea of quantum confinement and the relevant length scales as-sociated with it. Then it will focus on experimental evidence for confinementin these systems. Lastly we will discuss a few applications of quantum dotsto lasers and biology.2 ConfinementAdvances in surface and subsurface imagaing techniques have really helpedadvance nanoscience over the last ten years. Techniques such as scanning1Figure 1: This figure shows a cartoon of how the density of states of amaterial would change as the dimenstionality is reduced. The usual band-like structure is seen in 3-D, in 2-D we see steps, in 1-D lines begin to developand by 0-D we see an atom like DOS[?]tunneling microscopes (STM), atomic force microscopes (AFM), near-fieldscanning optical microscopes (NSOM) and scanning transmission electronmicroscopes (STEM) allow scientists to have to resolution small enough tonow resolve dots that have nm diameters. So you made a small dot, nowwhat? The question is what is the dimensionality of this dot. Here dimen-sionality of a material means how many dimensions do the carriers of thematerial act as free carriers. For example in a nanowire the electrons orholes only act a free carriers in one direction. In a dot none of the carriersact as free carriers in any direction. As the dimensionality is reduced thedensity of states changes drastically[?]. In 0-D the density of states of thematerial looks very much like an atom, a topic which will be discussed later.The ExcitonWhat is the relevant length scale for confinement? Optical exitations ina semiconductor should require a minimum energy equal to the band gap,but exitations are seen just below this energy. This exitation is a boundelectron-hole pair. This is because the pair bound and therefore it requiresless energy to excite it. This pair is called an exciton and has a lot ofproperties similar to the hydrogen atom and like the hydrogen atom theexiton has a Bohr diameter. This length is material dependent and whenthe size of the material becomes comperable to the exciton Bohr diameterconfinement effects become important.If the size of the dot is 3-10 times the exciton Bohr diameter the dot issaid to be in the week confinement regmine, but if it is smaller the dot is inthe strong confinement regime[?].2Figure 2: Shown is a table of exciton Bohr diameters. This is the relevantlength scale for confinement. Clearly it is material dependent.Observing ConfinementThere are a varitey of ways to experimentally observe confinement. Justan image of a small dot is not enough to say that there is quantum confine-ment present. This paper will discuss optical absorption, raman scatteringand photoluminescence spectroscopy experiments. Optical absorption is away to directly measure the band gap of a material. If a material is experi-ence confinement effects there should be a shift of the band gap edge towardthe blue wavelengths. As seen in figure ? Bukowski et al. present the opticalabsorption of Ge quantum dots in a SiO2matrix. There is a clear shift in theband edge toward shorter wavelengths as the size of the dot decreases. Theamount of blue shift due to size effects is a material dependent phenomona.Ge is shown here because it has a very large blue shift. The amount of shiftis due to the shape of the band gap.Another important technique for determining if the dots that are syn-thesized are quantumly confined or not is Raman vibrational spectroscopy.Raman spectroscopy occurs when light is shinned onto a sample and it ex-cites vibrational modes. This casuses the light to lose energy and changewavelength and is then detected. A strong narrow peak is a key indicator of3Figure 3: Here Bukowski et al. present optical data of Ge quantum dots. Aclear blue shift of the band edge is seen. It is also clearly dependent on thesize of the dots[?].a crystalline sample. As a nanocrystal starts to feel the effects of confinementthe Raman spectrum broadens. In figure ? we can see the Raman shift ofseveral different sizes of Ge dots. There is also a shift of the peak but oftentimes that feature is missing due to surface strain.The last experimental technique this paper will discuss is photolumines-cence spectroscopy. In photoluminescence spectroscopy a laser is tuned to aspecific energy that then excites carriers in the quantum dots and when theexcitations recombine photons are emitted and then measured. As the dotsget smaller the photoluminescence spectrum broadens and becomes spikey.Some very clean systems even have very narrow photoluminescence peaksand can be used to make quantum dot lasers[?].3 LasersThe atomic like density of states a quantum dot has is ideal for creating solidstate lasers with single narrow excitation modes. Also because the positionof the descrete peaks in the density of states is a function of size it shouldalso make the excitation modes tuneable. Also it is hopefully possible tocreate quantum dot lasers that have very low theashold current densities.These lasers are often used to make infrared lasers that may be important to4Figure 4: Here we see Raman data for several different sizes of Ge quantumdots. We see a clear broadening of the peak as well as a shift toward the laserwavelength. This feature is counter ballenced often times by surface strainso it is sometimes absent[?].Figure 5: Here we see the photoluminescence peak broaden and becomespikey which shows the 0-D behavior of this material[?].5Figure 6: Here we see the photoluminescence peak of InP quantum dots thatare used for lasers. We see a very narrow photoluminescence peak that isvery spike like a hallmark of 0-D behavior[?].the communications industry. One of the problems seems to be that the QDlasers have large threshold current densities, though smaller than quantumwell lasers now[?]. This paper will discuss the findings of two papers. Firstin 1998 an QD laser made from GeAs dots was synthesised. At 79 K